Broadcast Domination Algorithms for Interval Graphs, Series-Parallel Graphs, and Trees
نویسندگان
چکیده
Broadcast domination assigns an integer value f(u) 0 to each vertex u of a given graph, such that every vertex u with f(u) = 0 is within distance f(v) from a vertex v with f(v) > 0. We can regard the vertices v with f(v) > 0 as broadcast stations, each having a transmission power that might be di erent from the powers of other stations. The optimal broadcast domination problem seeks to minimize the sum of the costs of the broadcasts assigned to the vertices of the graph. We present dynamic programming algorithms that solve the optimal broadcast domination problem for the rst classes of graphs with non-trivial solutions: interval graphs, series-parallel graphs, and trees. We also show that optimal broadcast domination is equivalent to optimal domination on proper interval graphs.
منابع مشابه
Broadcast Domination on Block Graphs in Linear Time
A broadcast domination on a graph assigns an integer value f(u) ≥ 0 to each vertex u, such that every vertex u with f(u) = 0 is within distance f(v) from a vertex v with f(v) > 0. The Broadcast Domination problem seeks to compute a broadcast domination where the sum of the assigned values is minimized. We show that Broadcast Domination can be solved in linear time on block graphs. For general g...
متن کاملRoman domination excellent graphs: trees
A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...
متن کاملParallel Algorithms for Connected Domination Problem on Interval and Circular-arc Graphs
A connected domination set of a graph is a set of vertices such that every vertex not in is adjacent to and the induced subgraph of is connected. The minimum connected domination set of a graph is the connected domination set with the minimum number of vertices. In this paper, we propose parallel algorithms for finding the minimum connected domination set of interval graphs and circular-arc gra...
متن کاملIndependent domination in directed graphs
In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...
متن کاملTenacity and some other Parameters of Interval Graphs can be computed in polynomial time
In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined. In general, computing the tenacity o...
متن کامل